I think that mathematically equal temperament didn't come into use until the modern piano with an iron frame, though I don't know how pipe organs were tuned. At

I think that mathematically equal temperament didn't come into use until the modern piano with an iron frame, though I don't know how pipe organs were tuned. At the time of Bach, a keyboard instrument would go out of tune quickly, so a musician had to be able to tune their own instrument quickly, before every performance. Modern piano tuning is a specialized skill. Temperament methods evolved towards ever-better approximations of equal temperament. They all had names. Bach's "Well Tempered Klavier" was written for an instrument tuned in the Well temperament, and explored the unique tone quality of each key. String and wind instruments can't be played in tune consistently enough to worry about temperament. And musicians will push notes slightly sharp or flat for emphasis. On the cello, I was taught to slightly stretch whole-step intervals, and squeeze half-step intervals together when playing scales. It made a major scale sound "more major" for instance. Every wind instrument has one or two notes that are known to be bad and must be corrected on the fly, though it's less noticeable on faster passages. The musicians play in tune by listening to one another. Fretted instruments in Bach's time were an odd situation. Gut strings vary in density along their length, and go out of tune as they age. The viola da gamba had frets, but they were movable and required periodic adjustment. Even the temperament on a modern steel-stringed guitar is approximate. The compensated bridge is an attempt to correct the scale, but it's not perfect. And it's not systematically tempered, as in, adjacent octaves are not in tune with one another.